Linear Decision Fusion based Cooperative Spectrum Sensing in Cognitive Radio Networks Nima Reisi, Vahid Jamali, Mahmoud Ahmadian Faculty of Electrical and Computer Engineering K. N. Toosi University of Technology Tehran, Iran reisi.nima@ee.kntu.ac.ir, v jamali k@ee.kntu.ac.ir, mahmoud@eetd.kntu.ac.ir Abstract—In this paper, we consider the problem of cooper- ative spectrum sensing in a centralized cognitive radio network and propose a method to linearly combine the local decisions of secondary nodes, known as cognitive users, when the sensing and reporting channels are both experience fading. To be more specific, the problem of decision fusion is considered by the assumption that the primary signal is unknown deterministic signal with known power, sensing channel is assumed to be subjected to correlated lognormal shadow-fading and reporting channel is modeled as a binary symmetric channel with known error probability. Simulation results confirmed the effectiveness of the low complexity proposed algorithm. Index Terms—Cognitive radio, cooperative spectrum sensing, lognormal shadow-fading, decision fusion, deflection criterion I. I NTRODUCTION Cognitive Radio (CR)-based communication is an emerging technology to mitigate the scarcity of spectrum by utilizing the under-utilized bands preliminary assigned to licensed users. This task is performed by sensing the spectrum and detecting the unused portions of licensed bands. To avoid harmful interference to licensed (or primary) users operation, Cognitive Users (CUs) should firstly sense the spectrum and only if no active user is detected, start to communicate in the band. Hence, spectrum sensing is one of the key enabling functionalities of the CR technology. Among various spectrum sensing methods such as matched filter [1], feature detection [2] and wavelet detection [3], energy detection [1], [4], [5] is the most common method due to its low computational complexity which is also the utilized method in this paper. Severe fading, shadowing or blocking in the CR sensing channel can degrade sensing performance rapidly. To over- come these challenges, cooperative spectrum sensing (CSS) has been investigated in which different CRs collaboratively sense the spectrum band to increase the reliability of sensing results [6]. It is shown that compare to Rayleigh fading, shadowing effects are more important to be considered in design of a CSS framework [7]. However, most of papers analyze the CSS performance under Rayleigh (or the more general fading model i.e., Nakagami) fading [4], [5], [8]. In this paper, we will assume that sensing channel is subjected to correlated lognormal shadowing, as the most common model for shadowing [7], [9], [10]. Beside sensing channel, reporting channel on which CUs transmit their local observations/decisions to a central entity called fusion center (FC) is also noisy and the assumption of ideal reporting channel used in many papers is not practical. Here, we model the reporting channel as a binary symmetric channel (BSC) with known error probability [11]. Another important problem is energy detection-based spec- trum sensing is that its performance is highly related to the noise variance which is always known up to some degrees of accuracy. However, many papers assume that the noise variance is known precisely. To address this uncertainty, we model the noise as a zero-mean white noise with uncertainty in its variance [12]. CUs can share their observations or functions of them with each other. Although collaborating based on the received sig- nals in different CRs will lead us to higher performance [9], a high reporting channel bandwidth is also needed which causes this method to be impractical. Hence, in practice it is more common to use methods with lower reporting bandwidth in which CUs locally decide about the presence of primary user and then share their decisions with each other. These decisions can be hard decisions [6] (one bit) or soft decisions [13] (more than one bit up to the whole energy). Here, we assume the method with the least required reporting bandwidth, i.e. one- bit cooperation. Fusing the decisions is also another important challenge that should be considered. Fusing the correlated observations are studied in [14], [15]. However, these methods need the knowledge of all the mutual moments of local decisions which is complex and cannot easily used in practical scenarios. Therefore, finding a simpler fusion rule for correlated obser- vations is considered in this paper. Consequently, by assuming correlated lognormal shadowing in sensing channel, noisy reporting channel, and uncertainty in noise power estimation, our aim is to propose a low- complexity but efficient method to calculate the weights of linear fusing of local decisions. The rest of the paper is organized as follows: In section II, the system model is introduced. Section III is dedicated to the formulation of our problem consisting of received energies,